TSTP Solution File: SEV095^5 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEV095^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.bAYuKJJTLo true

% Computer : n028.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 19:59:35 EDT 2023

% Result   : Theorem 88.41s 12.02s
% Output   : Refutation 88.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   26
% Syntax   : Number of formulae    :  118 (   1 unt;  15 typ;   0 def)
%            Number of atoms       : 1149 (   2 equ; 203 cnn)
%            Maximal formula atoms :   25 (  11 avg)
%            Number of connectives : 5767 ( 172   ~; 435   |;  38   &;4792   @)
%                                         (   0 <=>;  45  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (  16 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  : 1168 (1168   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  15 usr;   6 con; 0-6 aty)
%                                         ( 280  !!;   5  ??;   0 @@+;   0 @@-)
%            Number of variables   :  315 (  14   ^; 285   !;   4   ?; 315   :)
%                                         (  12  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf('#sk9_type',type,
    '#sk9': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).

thf('#sk2_type',type,
    '#sk2': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).

thf('#form10_type',type,
    '#form10': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $o ).

thf('#sk1_type',type,
    '#sk1': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).

thf('#sk4_type',type,
    '#sk4': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).

thf('#sk7_type',type,
    '#sk7': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).

thf('#sk5_type',type,
    '#sk5': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).

thf('#sk8_type',type,
    '#sk8': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).

thf('#sk6_type',type,
    '#sk6': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).

thf('#sk3_type',type,
    '#sk3': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).

thf(s_comb_type,type,
    '#S': 
      !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( A > B ) > A > C ) ).

thf(c_comb_type,type,
    '#C': 
      !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > B > A > C ) ).

thf(b_comb_type,type,
    '#B': 
      !>[A: $tType,B: $tType,C: $tType] : ( ( A > B ) > ( C > A ) > C > B ) ).

thf(k_comb_type,type,
    '#K': 
      !>[A: $tType,B: $tType] : ( B > A > B ) ).

thf(i_comb_type,type,
    '#I': 
      !>[A: $tType] : ( A > A ) ).

thf(cTHM122C_pme,conjecture,
    ? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ! [Xu: $i > $o,Xv: $i > $o] :
          ( ! [Xw_2: $i] :
              ( ( Xr_27 @ Xu @ Xv @ Xw_2 )
              | ( Xr_28 @ Xu @ Xv @ Xw_2 ) )
         => ! [Xz: $i] :
              ( ( Xu @ Xz )
             => ( Xv @ Xz ) ) )
      & ! [Xx: $i > $o,Xw_2: $i] :
          ( ( Xr_27 @ Xx @ Xx @ Xw_2 )
          | ( Xr_28 @ Xx @ Xx @ Xw_2 ) )
      & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
          ( ( ! [Xw_2: $i] :
                ( ( Xr_27 @ Xy @ Xz @ Xw_2 )
                | ( Xr_28 @ Xy @ Xz @ Xw_2 ) )
            & ! [Xw_2: $i] :
                ( ( Xr_27 @ Xx @ Xy @ Xw_2 )
                | ( Xr_28 @ Xx @ Xy @ Xw_2 ) ) )
         => ! [Xw_2: $i] :
              ( ( Xr_27 @ Xx @ Xz @ Xw_2 )
              | ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
        ( ! [Xu: $i > $o,Xv: $i > $o] :
            ( ! [Xw_2: $i] :
                ( ( Xr_27 @ Xu @ Xv @ Xw_2 )
                | ( Xr_28 @ Xu @ Xv @ Xw_2 ) )
           => ! [Xz: $i] :
                ( ( Xu @ Xz )
               => ( Xv @ Xz ) ) )
        & ! [Xx: $i > $o,Xw_2: $i] :
            ( ( Xr_27 @ Xx @ Xx @ Xw_2 )
            | ( Xr_28 @ Xx @ Xx @ Xw_2 ) )
        & ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
            ( ( ! [Xw_2: $i] :
                  ( ( Xr_27 @ Xy @ Xz @ Xw_2 )
                  | ( Xr_28 @ Xy @ Xz @ Xw_2 ) )
              & ! [Xw_2: $i] :
                  ( ( Xr_27 @ Xx @ Xy @ Xw_2 )
                  | ( Xr_28 @ Xx @ Xy @ Xw_2 ) ) )
           => ! [Xw_2: $i] :
                ( ( Xr_27 @ Xx @ Xz @ Xw_2 )
                | ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) ) ),
    inference('cnf.neg',[status(esa)],[cTHM122C_pme]) ).

thf(zip_derived_cl0,plain,
    ~ ( ??
      @ ^ [Y0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
          ( ??
          @ ^ [Y1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
              ( ( !!
                @ ^ [Y2: $i > $o] :
                    ( !!
                    @ ^ [Y3: $i > $o] :
                        ( ( !!
                          @ ^ [Y4: $i] :
                              ( ( Y1 @ Y2 @ Y3 @ Y4 )
                              | ( Y0 @ Y2 @ Y3 @ Y4 ) ) )
                       => ( !!
                          @ ^ [Y4: $i] :
                              ( ( Y2 @ Y4 )
                             => ( Y3 @ Y4 ) ) ) ) ) )
              & ( !!
                @ ^ [Y2: $i > $o] :
                    ( !!
                    @ ^ [Y3: $i] :
                        ( ( Y1 @ Y2 @ Y2 @ Y3 )
                        | ( Y0 @ Y2 @ Y2 @ Y3 ) ) ) )
              & ( !!
                @ ^ [Y2: $i > $o] :
                    ( !!
                    @ ^ [Y3: $i > $o] :
                        ( !!
                        @ ^ [Y4: $i > $o] :
                            ( ( ( !!
                                @ ^ [Y5: $i] :
                                    ( ( Y1 @ Y3 @ Y4 @ Y5 )
                                    | ( Y0 @ Y3 @ Y4 @ Y5 ) ) )
                              & ( !!
                                @ ^ [Y5: $i] :
                                    ( ( Y1 @ Y2 @ Y3 @ Y5 )
                                    | ( Y0 @ Y2 @ Y3 @ Y5 ) ) ) )
                           => ( !!
                              @ ^ [Y5: $i] :
                                  ( ( Y1 @ Y2 @ Y4 @ Y5 )
                                  | ( Y0 @ Y2 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1,plain,
    ~ ( ?? @ ( '#B' @ ?? @ ( '#S' @ ( '#B' @ '#S' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ '#S' @ ( '#B' @ (=>) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ ( '#C' @ '#S' @ '#I' ) ) ) ) ) @ ( '#C' @ '#S' @ '#I' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lams2combs,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl2,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ~ ( ?? @ ( '#S' @ ( '#S' @ ( '#B' @ (&) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ '#S' @ ( '#B' @ (=>) ) ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ ( '#C' @ '#S' @ '#I' ) ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) ) ) ) @ X2 ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) ) ) ) @ X2 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl3,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ~ ( ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ '#S' @ ( '#B' @ (=>) ) ) ) ) ) )
        & ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
        & ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl4,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ '#S' @ ( '#B' @ (=>) ) ) ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl5,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk1' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk1' @ X2 @ X4 ) ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#sk1' @ X2 @ X4 ) ) ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl6,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) ) ) )
         => ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#sk1' @ X2 @ X4 ) ) @ ( '#sk2' @ X2 @ X4 ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl8,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#sk1' @ X2 @ X4 ) ) @ ( '#sk2' @ X2 @ X4 ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl10,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
         => ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl13,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl16,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( !! @ ( '#B' @ !! @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl19,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ ( '#B' @ (&) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) ) ) ) ) @ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl22,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
            & ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) )
         => ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl28,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl37,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl49,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl61,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl49]) ).

thf(zip_derived_cl73,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
      | ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl61]) ).

thf(zip_derived_cl7,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl9,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl11,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl14,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( !! @ ( '#B' @ !! @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl17,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ ( '#B' @ (&) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) ) ) ) ) @ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl20,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
            & ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) )
         => ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl24,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl31,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl40,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl52,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ~ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl64,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
      | ~ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl52]) ).

thf(zip_derived_cl76,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( '#form10' @ X2 @ X4 )
      | ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl88,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( '#form10' @ X2 @ X4 )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl73,zip_derived_cl76]) ).

thf(zip_derived_cl27,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
        & ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl35,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl46,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl58,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl46]) ).

thf(zip_derived_cl70,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl85,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
      | ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl70]) ).

thf(zip_derived_cl76_001,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( '#form10' @ X2 @ X4 )
      | ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl93,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( '#form10' @ X2 @ X4 )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl85,zip_derived_cl76]) ).

thf(zip_derived_cl12,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl15,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( !! @ ( '#B' @ !! @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl18,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ ( '#B' @ (&) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) ) ) ) ) @ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl21,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
            & ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) )
         => ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl26,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl34,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl45,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl57,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl69,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
      | ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl76_002,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( '#form10' @ X2 @ X4 )
      | ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl84,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( '#form10' @ X2 @ X4 )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl69,zip_derived_cl76]) ).

thf(zip_derived_cl25,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
        & ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl32,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl42,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl54,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl42]) ).

thf(zip_derived_cl66,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl81,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
      | ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl66]) ).

thf(zip_derived_cl76_003,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( '#form10' @ X2 @ X4 )
      | ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl91,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( '#form10' @ X2 @ X4 )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl81,zip_derived_cl76]) ).

thf(zip_derived_cl36,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl47,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl59,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl71,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl59]) ).

thf(zip_derived_cl86,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
      | ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl71]) ).

thf(zip_derived_cl76_004,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( '#form10' @ X2 @ X4 )
      | ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl94,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( '#form10' @ X2 @ X4 )
      | ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl86,zip_derived_cl76]) ).

thf(zip_derived_cl33,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl43,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl55,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl67,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl82,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
      | ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl67]) ).

thf(zip_derived_cl76_005,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( '#form10' @ X2 @ X4 )
      | ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl92,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( '#form10' @ X2 @ X4 )
      | ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl82,zip_derived_cl76]) ).

thf(zip_derived_cl41,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl53,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl41]) ).

thf(zip_derived_cl65,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
      | ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl53]) ).

thf(zip_derived_cl76_006,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( '#form10' @ X2 @ X4 )
      | ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl80,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ~ ( '#form10' @ X2 @ X4 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl65,zip_derived_cl76]) ).

thf(zip_derived_cl76_007,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( '#form10' @ X2 @ X4 )
      | ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl78,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
      | ( '#form10' @ X2 @ X4 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl76]) ).

thf(zip_derived_cl324,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X2: $i] :
      ( ~ ( X1 @ ( '#sk4' @ X1 @ X0 ) @ ( '#sk6' @ X1 @ X0 ) @ ( '#sk7' @ X1 @ X0 ) )
      | ( X0 @ ( '#sk1' @ X1 @ X0 ) @ ( '#sk2' @ X1 @ X0 ) @ X2 )
      | ( X1 @ ( '#sk1' @ X1 @ X0 ) @ ( '#sk2' @ X1 @ X0 ) @ X2 )
      | ~ ( X1 @ ( '#sk8' @ X1 @ X0 ) @ ( '#sk8' @ X1 @ X0 ) @ ( '#sk9' @ X1 @ X0 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl80,zip_derived_cl78]) ).

thf(zip_derived_cl23,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
        & ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl29,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl38,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
      ( ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 )
      | ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl50,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
      ( ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 )
      | ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl62,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 )
      | ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl74,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
      ( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
      | ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 )
      | ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl62]) ).

thf(zip_derived_cl76_008,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( '#form10' @ X2 @ X4 )
      | ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl89,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
      ( ~ ( '#form10' @ X2 @ X4 )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 )
      | ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl74,zip_derived_cl76]) ).

thf(zip_derived_cl671,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i] :
      ( ( ( X0 @ ( '#sk5' @ X2 @ X0 ) @ ( '#sk6' @ X2 @ X0 ) @ X1 )
       != ( X0 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 ) )
      | ( X2 @ ( '#sk5' @ X2 @ X0 ) @ ( '#sk6' @ X2 @ X0 ) @ X1 )
      | ( X2 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 )
      | ( X0 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 )
      | ~ ( '#form10' @ X2 @ X0 ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl89]) ).

thf(zip_derived_cl735,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i] :
      ( ( X0 @ ( '#sk5' @ X2 @ X0 ) @ ( '#sk6' @ X2 @ X0 ) @ X1 )
      | ( X2 @ ( '#sk5' @ X2 @ X0 ) @ ( '#sk6' @ X2 @ X0 ) @ X1 )
      | ( X2 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 )
      | ( X0 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 )
      | ~ ( '#form10' @ X2 @ X0 ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl671]) ).

thf(zip_derived_cl78_009,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ~ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
      | ( '#form10' @ X2 @ X4 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl76]) ).

thf(zip_derived_cl30,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
      ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl39,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
      ( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 )
      | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl51,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
      ( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 )
      | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 )
      | ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl63,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
      ( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 )
      | ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl75,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
      ( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
      | ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 )
      | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl63]) ).

thf(zip_derived_cl76_010,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
      ( ( '#form10' @ X2 @ X4 )
      | ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
          | ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl90,plain,
    ! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
      ( ~ ( '#form10' @ X2 @ X4 )
      | ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
      | ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 )
      | ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl75,zip_derived_cl76]) ).

thf(zip_derived_cl1107,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i] :
      ( ( ( X0 @ ( '#sk4' @ X2 @ X0 ) @ ( '#sk5' @ X2 @ X0 ) @ X1 )
       != ( X0 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 ) )
      | ( X2 @ ( '#sk4' @ X2 @ X0 ) @ ( '#sk5' @ X2 @ X0 ) @ X1 )
      | ( X2 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 )
      | ( X0 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 )
      | ~ ( '#form10' @ X2 @ X0 ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl90]) ).

thf(zip_derived_cl1171,plain,
    ! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i] :
      ( ( X0 @ ( '#sk4' @ X2 @ X0 ) @ ( '#sk5' @ X2 @ X0 ) @ X1 )
      | ( X2 @ ( '#sk4' @ X2 @ X0 ) @ ( '#sk5' @ X2 @ X0 ) @ X1 )
      | ( X2 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 )
      | ( X0 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 )
      | ~ ( '#form10' @ X2 @ X0 ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl1107]) ).

thf(zip_derived_cl4942,plain,
    $false,
    inference(eprover,[status(thm)],[zip_derived_cl88,zip_derived_cl93,zip_derived_cl84,zip_derived_cl91,zip_derived_cl94,zip_derived_cl92,zip_derived_cl324,zip_derived_cl735,zip_derived_cl78,zip_derived_cl1171]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEV095^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.bAYuKJJTLo true
% 0.13/0.34  % Computer : n028.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug 24 04:04:19 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Running portfolio for 300 s
% 0.13/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35  % Number of cores: 8
% 0.21/0.35  % Python version: Python 3.6.8
% 0.21/0.35  % Running in HO mode
% 0.21/0.66  % Total configuration time : 828
% 0.21/0.66  % Estimated wc time : 1656
% 0.21/0.66  % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.72  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.76  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.76  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.76  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.77  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 88.41/12.02  % Solved by lams/40_b.comb.sh.
% 88.41/12.02  % done 187 iterations in 11.161s
% 88.41/12.02  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 88.41/12.02  % SZS output start Refutation
% See solution above
% 88.41/12.02  
% 88.41/12.02  
% 88.41/12.02  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 88.41/12.02  % Terminating...
% 89.09/12.16  % Runner terminated.
% 89.12/12.18  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------